The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km from the asteroid's center. Eros is roughly box-shaped, with dimensions 40 km 6 km 6 km. Assume Eros has a density (mass/volume) of about 2.3 103 kg/m3.
What will be the period of NEAR as it orbits Eros?
If Eros were a sphere with the same mass and density, what would its radius be?
What would g be at the surface of this spherical Eros?